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ISEN 315 Spring 2011 Dr. Gary Gaukler

ISEN 315 Spring 2011 Dr. Gary Gaukler. Two-equation Smoothing Model. Add linear trend: Assume D t = m + t G + e t S t = a D t + (1- a ) [ S t-1 + 1 G t-1 ], where G t -1 = 1-period trend estimate. Two-equation Smoothing Model:. Update G by exponential smoothing:

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ISEN 315 Spring 2011 Dr. Gary Gaukler

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  1. ISEN 315Spring 2011Dr. Gary Gaukler

  2. Two-equation Smoothing Model Add linear trend: • Assume Dt = m + t G + et St = aDt + (1-a ) [St-1 + 1 Gt-1], where Gt -1 = 1-period trend estimate

  3. Two-equation Smoothing Model: Update G by exponential smoothing: Gt = b (St - St-1) +(1 - b)Gt-1 Then forecast is: Ft,t+t = St + tGt

  4. Introduction to Aggregate Planning • Goal: To plan gross work force levels and set firm-wide production plans, based on predicted demand for aggregate units.

  5. Hierarchy of Planning • Forecast of aggregate demand over time horizon • Aggregate Production Plan: determine aggregate production and workforce levels over time horizon • Master Production Schedule: Disaggregate the aggregate plan and determine per-item production levels • Materials Requirements Planning: Detailed schedule for production/replenishment activities

  6. Why Aggregate?

  7. Aggregate Units The method is based on notion of aggregate units. They may be • Actual units of production • Weight (tons of steel) • Volume (gallons of gasoline) • Dollars (Value of sales) • Fictitious aggregate units

  8. Example of fictitious aggregate units One plant produced 6 models of washing machines: Model # hrs. Price % sales A 5532 4.2 285 32 K 4242 4.9 345 21 L 9898 5.1 395 17 L 3800 5.2 425 14 M 2624 5.4 525 10 M 3880 5.8 725 06 Question: How do we define an aggregate unit here?

  9. Example continued • Notice: Price is not necessarily proportional to worker hours (i.e., cost): why? • One method for defining an aggregate unit: requires: .32(4.2) + .21(4.9) + . . . + .06(5.8) = 4.8644 worker hours.

  10. Overview of the Problem Suppose that D1, D2, . . . , DT are the forecasts of demand for aggregate units over the planning horizon (T periods.) The problem is to determine both work force levels (Wt) and production levels (Pt ) to minimize total costs over the T period planning horizon.

  11. Relevant Costs • Smoothing Costs • changing size of the work force • changing number of units produced • Holding Costs • primary component: opportunity cost of investment • Shortage Costs • Cost of demand exceeding stock on hand. Why should shortages be an issue if demand is known? • Other Costs: payroll, overtime, subcontracting.

  12. Prototype Aggregate Planning Example The washing machine plant is interested in determining work force and production levels for the next 8 months. Forecasted aggregate demands for Jan-Aug. are: 420, 280, 460, 190, 310, 145, 110, 125. Starting inventory at the end of December is 200 and the firm would like to have 100 units on hand at the end of August. Find monthly production levels.

  13. Step 1: Determine “net” demand. Month Net Predicted Cum. Net Demand Demand 1(Jan) 220 220 2(Feb) 280 500 3(Mar) 460 960 4(Apr) 190 1150 5(May) 310 1460 6(June) 145 1605 7(July) 110 1715 8(Aug) 225 1940

  14. Step 2. Graph Cumulative Net Demand to Find Plans Graphically

  15. Constant Work Force Plan Suppose that we are interested in determining a production plan that doesn’t change the size of the workforce over the planning horizon. How would we do that?

  16. Monthly Production = 1940/8 = 242.2 or rounded to 243/month. But: there are stockouts.

  17. How can we have a constant work force plan with no stockouts? Using the graph, find a straight line that lies completely above the cumulative net demand curve:

  18. From the previous graph, we see that the cum. net demand curve is crossed at period 3, so that monthly production is 960/3 = 320. Ending inventory each month is found from: Month Cum. Net. Dem. Cum. Prod. Invent. 1(Jan) 220 320 100 2(Feb) 500 640 140 3(Mar) 960 960 0 4(Apr.) 1150 1280 130 5(May) 1460 1600 140 6(June) 1605 1920 315 7(July) 1715 2240 525 8(Aug) 1940 2560 620

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